Hello,I am trying to come up with an idea for a science fair project (due in January) and one of the only ideas that interests me is the idea of trying to find mathematical patterns in music. I was considering either looking for patterns in 5 famous classical piano pieces, or patterns in pop songs over the decades. I had a few questions about this project idea, regardless of which genre I choose.1. How might I go about analyzing these songs without getting too complex? I was thinking of looking for ratios of treble clef to base clef notes (in classical music) or popular chord progressions (in pop songs). What other venues might I try?2. How would I write a long enough (3-4 pages) research paper on a topic like this? What would I want to include?

The ways that you've mentioned- treble clef to bass clef and chord progressions- seem like a good place to start. I'd suggest also looking up the 'Circle of Fifths', which is a diagram that could help you break down the music into different categories based on note transitions. As for chords, there is usually a base note out of which the chord is constructed; looking up 'Chord Theory' might tell you more, as I'm not too familiar with music theory.

Alternately, you could pick out one series of notes as being the melody, then record those notes as numbers- A to 1, B to 2, and so on and so forth, with flats and sharps being decimals; A sharp would be 1.5, in that sense. After turning the music into a string of numbers, you could code in essentially any kind of analysis that you were interested in- frequency of different interval jumps, frequency of discordant notes, and so on.

I'm typing up this reply in a little bit of a hurry, so I may have made something unclear; if so, please don't hesitate to ask!

Hope this helped, and good luck,

-Vysarge

~~~~~~~~~~~~~Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.-Richard Feynman

Not being a musical expert, I would suggest that you consult with a music teacher in your school to get suggestions on candidates of music to be analyzed. I would suggest a fairly broad range of music to get diverse data for your project.

Some suggestions for inclusion in your project report:

1. Background on music analyzed--Why was the particular music chosen? How is it special? 2. Technical limits of instrumentation--Where there any limits on how music was produced at the particular time of the composition that forced the production of a certain type of music?3. Patterns of music meaning--Is certain music used for particular meanings (e.g. drums connotate excitement)?4. Summary chart--perhaps a summary of your analysis should be provided in tabular form for easy comparison.

This list is not exhaustive and is intended to start your own thought process. Suggest that you include your music teacher in your team as you proceed with this very interesting project.

Thanks for your ideas, Akbarkhan! I am homeschooled so finding a music teacher to help me could be complicated, but I will definitely consider the ideas for analysis that you presented. The part of this project that I am most struggling with is ideas for writing a long enough paper. Does anyone have any ideas of what I might write about in my research report? Thanks again!--Nicole

The research paper is intended to provide the theory and innovative ideas that went into your research project along with data collected and analyzed, conclusions reached, and lessons learned for those who may conduct similar projects in the future. The rule of thumb is to include enough information so that a person who is reviewing your project to understand what is your problem/issue that you were reviewing, how you applied established theory, and what are your resultant conclusions. I also suggest including a summary (sometimes called an abstract) in the beginning of your report.

A word of caution: There is a need to balance between the need for brevity and the desire to include all relevant data based on your judgment on what is required to get your thought process during the project across to the reader. Good luck.